Click here to close now.

Welcome!

Web 2.0 Authors: Carmen Gonzalez, Liz McMillan, Kevin Benedict, Aria Blog, John Treadway

Related Topics: Web 2.0

Web 2.0: Article

How Can Metcalfe's Law Be Updated for Web 2.0?

Metcalfe's Law is More Misunderstood Than Wrong

"Metcalfe's Law is Wrong," contended Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly recently in a much-discussed IEEE Spectrum article, in which they wrote: "Of all the popular ideas of the Internet boom, one of the most dangerously influential was Metcalfe's Law." Sim Simeonov disagrees.

The industry is at it again – trying to figure out what to make of Metcalfe’s Law. This time it’s IEEE Spectrum with a controversially titled “Metcalfe’s Law is Wrong”. The main thrust of the argument is that the value of a network grows O(nlogn) as opposed to O(n2). Unfortunately, the authors’ O(nlogn) suggestion is no more accurate or insightful than the original proposal.

There are three issues to consider:

  • The difference between what Bob Metcalfe claimed and what ended up becoming Metcalfe’s Law
  • The units of measurement
  • What happens with large networks

The typical statement of the law is “the value of a network increases proportionately with the square of the number of its users.” That’s what you’ll find at the Wikipedia link above. It happens to not be what Bob Metcalfe claimed in the first place. These days I work with Bob at Polaris Venture Partners. I have seen a copy of the original (circa 1980) transparency that Bob created to communicate his idea. IEEE Spectrum has a good reproduction, shown here.

The original Metcalfe's Law graph

The unit of measurement along the X-axis is “compatibly communicating devices”, not users. The credit for the “users” formulation goes to George Gilder who wrote about Metcalfe’s Law in Forbes ASAP on September 13, 1993. However, Gilder’s article talks about machines and not users. Anyway, both the “users” and “machines” formulations miss the subtlety imposed by the “compatibly communicating” qualifier, which is the key to understanding the concept.

Bob, who invented Ethernet, was addressing small LANs where machines are visible to one another and share services such as discovery, email, etc. He recalls that his goal was to have companies install networks with at least three nodes. Now, that’s a far cry from the Internet, which is huge, where most machines cannot see one another and/or have nothing to communicate about… So, if you’re talking about a smallish network where indeed nodes are “compatibly communicating”, I’d argue that the original suggestion holds pretty well.

The authors of the IEEE article take the “users” formulation and suggest that the value of a network should grow on the order of O(nlogn) as opposed to O(n2). Are they correct? It depends. Is their proposal a meaningful improvement on the original idea? No.

To justify the logn factor, the authors apply Zipf’s Law to large networks. Again, the issue I have is with the unit of measurement. Zipf’s Law applies to homogeneous populations (the original research was on natural language). You can apply it to books, movies and songs. It’s meaningless to apply it to the population of books, movies and songs put together or, for that matter, to the Internet, which is perhaps the most heterogeneous collection of nodes, people, communities, interests, etc. one can point to. For the same reason, you cannot apply it to MySpace, which is a group of sub-communities hosted on the same online community infrastructure (OCI), or to the Cingular / AT&T Wireless merger.

The main point of Metcalfe’s Law is that the value of networks exhibits super-linear growth. If you measure the size of networks in users, the value definitely does not grow O(n2) but I’m not sure O(nlogn) is a significantly better approximation, especially for large networks. A better approximation of value would be something along the lines of O(SumC(O(mclogmc))), where C is the set of homogeneous sub-networks/communities and mc is the size of the particular sub-community/network. Since the same user can be a member of multiple social networks, and since |C| is a function of N (there are more communities in larger networks), it’s not clear what the total value will end up being. That’s a Long Tail argument if you want one…

Very large networks pose a further problem. Size introduces friction and complicates connectivity, discovery, identity management, trust provisioning, etc. Does this mean that at some point the value of a network starts going down (as another good illustration from the IEEE article shows)? It depends on infrastructure. Clients and servers play different roles in networks. (For more on this in the context of Metcalfe’s Law, see Integration is the Killer App, an article I wrote for XML Journal in 2003, having spent less time thinking about the problem ;-) ). P2P sharing, search engines and portals, anti-spam tools and federated identity management schemes are just but a few examples of the myriad of technologies that have all come about to address scaling problems on the Internet. MySpace and LinkedIn have very different rules of engagement and policing schemes. These communities will grow and increase in value very differently. That’s another argument for the value of a network aggregating across a myriad of sub-networks.

Bottom line, the article attacks Metcalfe’s Law but fails to propose a meaningful alternative.

More Stories By Simeon Simeonov

Simeon Simeonov is CEO of FastIgnite, where he invests in and advises startups. He was chief architect or CTO at companies such as Allaire, Macromedia, Better Advertising and Thing Labs. He blogs at blog.simeonov.com, tweets as @simeons and lives in the Greater Boston area with his wife, son and an adopted dog named Tye.

Comments (6) View Comments

Share your thoughts on this story.

Add your comment
You must be signed in to add a comment. Sign-in | Register

In accordance with our Comment Policy, we encourage comments that are on topic, relevant and to-the-point. We will remove comments that include profanity, personal attacks, racial slurs, threats of violence, or other inappropriate material that violates our Terms and Conditions, and will block users who make repeated violations. We ask all readers to expect diversity of opinion and to treat one another with dignity and respect.


Most Recent Comments
wsanders 08/13/06 08:41:43 AM EDT

I sort of see the key insight of Briscoe, Odlyzko, and Tilly that, if you are going to pull a function out of your ass, it makes more sense if the differential of the function flattens out rather than slopes linearly upwards forever, because there is ultimately a decreasing value of each connection as the number of connections increases.

So they were correct to pull a log function of of their ass, but they could have just as easily pulled out n*ln(n) or some other base. They made no attempt to "calibrate" the model.

A good insight is this quotation:

"If Metcalfe's Law were true, it would create overwhelming incentives for all networks relying on the same technology to merge, or at least to interconnect. These incentives would make isolated networks hard to explain. Consider two networks, each with n members. By Metcalfe's Law, each one's value is on the order of n 2, so the total value of both of these separate networks is roughly 2n 2. But suppose these two networks merge. Then we will effectively have a single network with 2n members, which, by Metcalfe's Law, will be worth (2n)2 or 4n 2--twice as much as the combined value of the two separate networks.

Surely it would require a singularly obtuse management, to say nothing of stunningly inefficient financial markets, to fail to seize this obvious opportunity to double total network value by simply combining the two."

Inflating these "synergies" was exactly what led to the Bombing Off of the Bubble.

MountainLogic 08/13/06 08:38:03 AM EDT

This all came about because Metcalfe was trying to make a case for networking (e.g., ethernet).

Back then the ethernet cards he was selling were expensive. The decision maker would go, "gee, if it cost $x to network two people why can't Bob just walk down the hall to Jan's office?" If X is greater then the cost of Bob "walking down the hall" (or snail mailing or flying...) then there is no busines case for installing a network. More to the point:
If the node cost, x, is $100 and there are 100 users, n, then the cost for the network is $10,000.

If the single user business value, v, of the network is $10 for one user then the ROI for different valuation methods is:

Linear: vn = $1,000 -- no business case, don't even think about it

Metcalf's Law: (n(n-1)=2)v = 49,500 -- winner

Metcalf's Law as misused by dot-bombers: N^2 * V = 100,000 -- "Proves" selling frozen mud on the net is a winner

As restated by the authors: n long (n) * v = 2000 -- no business case, but better than a flat linear

There really are two problems here. The scaling formula and setting the business value. If you set the business value for a single connection greater than the cost of the network then it is a no brainer, but back when Metcalfe was pushing networking that was a hard case to make.

Scott Allen 08/13/06 08:20:00 AM EDT

Metcalfe's Law has always been understood to mean "the theoretical potential value", since a very large number of the links between nodes will never be made.

This same idea can be applied to Reed's Law, which states that the potential value of social networks, i.e., those with self-organizing groups, grows as 2^N (actually, 2^N - N - 1). In reality, of course, this never even comes close, because real groups don't usually organize like that ("let's make a sub-group within our group that excludes one person", etc.).

Also, virtual groups, in particular, don't tend to break off into ad hoc sub-groups if they don't have the tools to do so, e.g., the participants in one thread don't typically say "Let's go create a new group to discuss this." It's theoretically possible, but only occasionally occurs. Of course, the participants in a particular thread can be considered a sort of ad hoc sub-group, in which case you might achieve something closer to the potential, but still...

Interesting stuff - thanks for the link.

Jon Rubin 08/13/06 08:05:56 AM EDT

Metcalfe's Law said that the value of a network, x, as it increases in network members, n, is described by the equation x=n^2.

In other words, it said the value of a network was proportional to the square of the network's users.

Instead, the IEEE article declares it should be x=n"log(n). My suspicion - and this has no basis in anything and I haven't even graphed it and my total knowledge of information theory is that it was started by a guy named Claude - is that Euler has to be involved somewhere and maybe x=n"ln(n) would be more correct.

Peter O'Kelly 08/13/06 08:03:17 AM EDT

insightful analysis

Johannes Ernst 08/13/06 07:58:19 AM EDT

Of course Metcalfe's Law is overstated! If I have a fax machine and somebody in central China, who I have never heard of and will never interact with, buys another fax machine, the value of the network will not grow proportionally to N (say, hundreds of millions: the number of fax machines in existence today) but by some much smaller number such as a couple of hundred at the maximum (the number of fax machines that person will ever send a fax to or receive a fax from)...

@ThingsExpo Stories
SYS-CON Events announced today that Intelligent Systems Services will exhibit at SYS-CON's 16th International Cloud Expo®, which will take place on June 9-11, 2015, at the Javits Center in New York City, NY. Established in 1994, Intelligent Systems Services Inc. is located near Washington, DC, with representatives and partners nationwide. ISS’s well-established track record is based on the continuous pursuit of excellence in designing, implementing and supporting nationwide clients’ mission-critical systems. ISS has completed many successful projects in Healthcare, Commercial, Manufacturing, ...
WebRTC is an up-and-coming standard that enables real-time voice and video to be directly embedded into browsers making the browser a primary user interface for communications and collaboration. WebRTC runs in a number of browsers today and is currently supported in over a billion installed browsers globally, across a range of platform OS and devices. Today, organizations that choose to deploy WebRTC applications and use a host machine that supports audio through USB or Bluetooth can use Plantronics products to connect and transit or receive the audio associated with the WebRTC session.
The best mobile applications are augmented by dedicated servers, the Internet and Cloud services. Mobile developers should focus on one thing: writing the next socially disruptive viral app. Thanks to the cloud, they can focus on the overall solution, not the underlying plumbing. From iOS to Android and Windows, developers can leverage cloud services to create a common cross-platform backend to persist user settings, app data, broadcast notifications, run jobs, etc. This session provides a high level technical overview of many cloud services available to mobile app developers, includi...
SYS-CON Events announced today that B2Cloud, a provider of enterprise resource planning software, will exhibit at SYS-CON's 16th International Cloud Expo®, which will take place on June 9-11, 2015, at the Javits Center in New York City, NY. B2cloud develops the software you need. They have the ideal tools to help you work with your clients. B2Cloud’s main solutions include AGIS – ERP, CLOHC, AGIS – Invoice, and IZUM
The WebRTC Summit 2015 New York, to be held June 9-11, 2015, at the Javits Center in New York, NY, announces that its Call for Papers is open. Topics include all aspects of improving IT delivery by eliminating waste through automated business models leveraging cloud technologies. WebRTC Summit is co-located with 16th International Cloud Expo, @ThingsExpo, Big Data Expo, and DevOps Summit.
SYS-CON Events announced today that Tufin, the market-leading provider of Security Policy Orchestration Solutions, will exhibit at SYS-CON's 16th International Cloud Expo®, which will take place on June 9-11, 2015, at the Javits Center in New York City, NY. As the market leader of Security Policy Orchestration, Tufin automates and accelerates network configuration changes while maintaining security and compliance. Tufin's award-winning Orchestration Suite™ gives IT organizations the power and agility to enforce security policy across complex, multi-vendor enterprise networks. With more than 1...
As enterprises move to all-IP networks and cloud-based applications, communications service providers (CSPs) – facing increased competition from over-the-top providers delivering content via the Internet and independently of CSPs – must be able to offer seamless cloud-based communication and collaboration solutions that can scale for small, midsize, and large enterprises, as well as public sector organizations, in order to keep and grow market share. The latest version of Oracle Communications Unified Communications Suite gives CSPs the capability to do just that. In addition, its integration ...
SYS-CON Events announced today that Cloudian, Inc., the leading provider of hybrid cloud storage solutions, will exhibit at SYS-CON's 16th International Cloud Expo®, which will take place on June 9-11, 2015, at the Javits Center in New York City, NY. Cloudian, Inc., is a Foster City, California - based software company specializing in cloud storage software. The main product is Cloudian, an Amazon S3-compliant cloud object storage platform, the bedrock of cloud computing systems, that enables cloud service providers and enterprises to build reliable, affordable and scalable cloud storage solu...
SYS-CON Events announced today that Gridstore™, the leader in hyper-converged infrastructure purpose-built to optimize Microsoft workloads, will exhibit at SYS-CON's 16th International Cloud Expo®, which will take place on June 9-11, 2015, at the Javits Center in New York City, NY. Gridstore™ is the leader in hyper-converged infrastructure purpose-built for Microsoft workloads and designed to accelerate applications in virtualized environments. Gridstore’s hyper-converged infrastructure is the industry’s first all flash version of HyperConverged Appliances that include both compute and storag...
SYS-CON Events announced today that IDenticard will exhibit at SYS-CON's 16th International Cloud Expo®, which will take place on June 9-11, 2015, at the Javits Center in New York City, NY. IDenticard™ is the security division of Brady Corp (NYSE: BRC), a $1.5 billion manufacturer of identification products. We have small-company values with the strength and stability of a major corporation. IDenticard offers local sales, support and service to our customers across the United States and Canada. Our partner network encompasses some 300 of the world's leading systems integrators and security s...
BroadSoft on Tuesday announced that it is a recipient of the 2014 Frost & Sullivan Market Leadership Award in the Hosted/Cloud Internet Protocol (IP) Telephony market for Latin America. According to Frost & Sullivan market research, the Latin America (LATAM) hosted/cloud Internet Protocol (IP) telephony market, including integrated unified communications and collaboration (UC&C) applications, is currently experiencing a rapid growth trajectory and is expected to exhibit a tenfold rise in annual revenues in the 2013-2020 period. With more than 600 cloud deployments internationally, BroadSoft w...
In 2015, 4.9 billion connected "things" will be in use. By 2020, Gartner forecasts this amount to be 25 billion, a 410 percent increase in just five years. How will businesses handle this rapid growth of data? Hadoop will continue to improve its technology to meet business demands, by enabling businesses to access/analyze data in real time, when and where they need it. Cloudera's Chief Technologist, Eli Collins, will discuss how Big Data is keeping up with today's data demands and how in the future, data and analytics will be pervasive, embedded into every workflow, application and infra...
Participants will reach the final if their IoT solution is liked. A community vote will determine the best solutions submitted in each country, after which an expert jury will select the national winners and the best international IoT solution. Each country's best solution can win a national marketing campaign worth up to €30,000 and become a partner in Deutsche Telekom's participating markets. The winning international solution can become partner of Deutsche Telekom Group across all eight countries and reach out to a potential of 10,8 million business customers. Deutsche Telekom Group has a...
Health care systems across the globe are under enormous strain, as facilities reach capacity and costs continue to rise. M2M and the Internet of Things have the potential to transform the industry through connected health solutions that can make care more efficient while reducing costs. In fact, Vodafone's annual M2M Barometer Report forecasts M2M applications rising to 57 percent in health care and life sciences by 2016. Lively is one of Vodafone's health care partners, whose solutions enable older adults to live independent lives while staying connected to loved ones. M2M will continue to gr...
SYS-CON Events announced today that Vicom Computer Services, Inc., a provider of technology and service solutions, will exhibit at SYS-CON's 16th International Cloud Expo®, which will take place on June 9-11, 2015, at the Javits Center in New York City, NY. They are located at booth #427. Vicom Computer Services, Inc. is a progressive leader in the technology industry for over 30 years. Headquartered in the NY Metropolitan area. Vicom provides products and services based on today’s requirements around Unified Networks, Cloud Computing strategies, Virtualization around Software defined Data Ce...
Dave will share his insights on how Internet of Things for Enterprises are transforming and making more productive and efficient operations and maintenance (O&M) procedures in the cleantech industry and beyond. Speaker Bio: Dave Landa is chief operating officer of Cybozu Corp (kintone US). Based in the San Francisco Bay Area, Dave has been on the forefront of the Cloud revolution driving strategic business development on the executive teams of multiple leading Software as a Services (SaaS) application providers dating back to 2004. Cybozu's kintone.com is a leading global BYOA (Build Your O...
VoxImplant has announced full WebRTC support in the newest versions of its Android SDK and iOS SDK. The updated SDKs, which enable audio and video calls on mobile devices, are now compatible with the WebRTC standard to allow any mobile app to communicate with WebRTC-enabled browsers, including Google Chrome, Mozilla Firefox, Opera, and, when available, Microsoft Spartan. The WebRTC-updated SDKs represent VoxImplant's continued leadership in simplifying the development of real-time communications (RTC) services for app developers. VoxImplant (built by Zingaya, the real-time communication servi...
What exactly is a cognitive application? In her session at 16th Cloud Expo, Ashley Hathaway, Product Manager at IBM Watson, will look at the services being offered by the IBM Watson Developer Cloud and what that means for developers and Big Data. She'll explore how IBM Watson and its partnerships will continue to grow and help define what it means to be a cognitive service, as well as take a look at the offerings on Bluemix. She will also check out how Watson and the Alchemy API team up to offer disruptive APIs to developers.
The IoT Bootcamp is coming to Cloud Expo | @ThingsExpo on June 9-10 at the Javits Center in New York. Instructor. Registration is now available at http://iotbootcamp.sys-con.com/ Instructor Janakiram MSV previously taught the famously successful Multi-Cloud Bootcamp at Cloud Expo | @ThingsExpo in November in Santa Clara. Now he is expanding the focus to Janakiram is the founder and CTO of Get Cloud Ready Consulting, a niche Cloud Migration and Cloud Operations firm that recently got acquired by Aditi Technologies. He is a Microsoft Regional Director for Hyderabad, India, and one of the f...
The 17th International Cloud Expo has announced that its Call for Papers is open. 17th International Cloud Expo, to be held November 3-5, 2015, at the Santa Clara Convention Center in Santa Clara, CA, brings together Cloud Computing, APM, APIs, Microservices, Security, Big Data, Internet of Things, DevOps and WebRTC to one location. With cloud computing driving a higher percentage of enterprise IT budgets every year, it becomes increasingly important to plant your flag in this fast-expanding business opportunity. Submit your speaking proposal today!